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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Expansivity and shadowing in linear dynamics

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Author(s):
Bernardes, Jr., Nilson C. [1] ; Cirilo, Patricia R. [2] ; Darji, Udayan B. [3, 4] ; Messaoudi, Ali [5] ; Pujals, Enrique R. [6]
Total Authors: 5
Affiliation:
[1] Univ Fed Rio de Janeiro, Inst Matemat, Dept Matemat Aplicada, Caixa Postal 68530, BR-21945970 Rio De Janeiro, RJ - Brazil
[2] Univ Fed Sao Paulo, Inst Ciencia & Tecnol, Ave Cesare Mansueto Giulio Lattes 1201, BR-12247014 Sao Jose Dos Campos, SP - Brazil
[3] Univ Louisville, Dept Math, Louisville, KY 40292 - USA
[4] Ashoka Univ, Dept Math, Rajiv Gandhi Educ City K 131029, Rai - India
[5] Univ Estadual Paulista, Dept Matemat, Rua Cristovao Colombo 2265, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil
[6] Inst Nacl Matemat Pura & Aplicada, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, RJ - Brazil
Total Affiliations: 6
Document type: Journal article
Source: Journal of Mathematical Analysis and Applications; v. 461, n. 1, p. 796-816, MAY 1 2018.
Web of Science Citations: 5
Abstract

In the early 1970's Eisenberg and Hedlund investigated relationships between expansivity and spectrum of operators on Banach spaces. In this paper we establish relationships between notions of expansivity and hypercyclicity, supercyclicity, Li-Yorke chaos and shadowing. In the case that the Banach space is c(0) or l(p) (1 <= p < infinity), we give complete characterizations of weighted shifts which satisfy various notions of expansivity. We also establish new relationships between notions of expansivity and spectrum. Moreover, we study various notions of shadowing for operators on Banach spaces. In particular, we solve a basic problem in linear dynamics by proving the existence of nonhyperbolic invertible operators with the shadowing property. This contrasts with the expected results for nonlinear dynamics on compact manifolds, illuminating the richness of dynamics of infinite dimensional linear operators. (C) 2017 Elsevier Inc. All rights reserved. (AU)

FAPESP's process: 13/24541-0 - Ergodic and qualitative theory of dynamical systems
Grantee:Claudio Aguinaldo Buzzi
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 11/11663-5 - Ergodic and algebraic properties for dynamical systems which preserves an infinite measure
Grantee:Patricia Romano Cirilo
Support Opportunities: Scholarships in Brazil - Post-Doctoral